Lesson planning 1 of TTC2-G3

The entire schedule of lesson study practice in this TTC is demonstrated in Table 22.

Since this TTC has already constructed their own practice schedule, the researcher respectively followed their program of planning a lesson on Monday afternoon and teaching the lesson on Tuesday morning. In the afternoon of March 18, 2019, four MTEs (KHL, VVL, VLV, & SLK) and one primary teacher (SMN) collaborated to plan a lesson. Before lesson planning 1 began, the researcher explained why he was visiting and how he would collect the data. Actually, they were already acquainted with the researcher from the preliminary survey the previous year.

Therefore, there was not any issue related to the data collection or the group’s collaboration with the researcher. Once they accepted the researcher’s objectives, they immediately proceeded with lesson planning.

Table 22. Schedule of lesson study practice at Pakse TTC

No Activities Number of participants Date

1 Planning 1 5 (4 MTEs, 1 Pri-T) March 18^th, 2019

2 Teaching 1 & reflection 1 5 (4 MTEs, 1 Pri-T) March 19^th, 2019 3 Researcher’s comments Individually right after the interviews

4 Planning 2 7 (6 MTEs, 1 Pri-T) March 25^th, 2019

5 Teaching 2 & reflection 2 6 (5 MTEs, 1 Pri-T) March 26^th, 2019

Their plaining began with the homeroom teacher, SMN, reporting on the latest lesson to the group; she had recently taught up to page 121 of Lesson 14, subtraction (cont.), but had not yet finished. If the lesson study continued from there, it would involve the exercise on page 122. Following the report, the group immediately started discussing student difficulties and mathematical problems. Regarding the previous lesson about subtraction, 12 - 3, KHL, the leader of the group, asked what SMN had already taught and if students could solve it via decomposition. SMN expressed that students could solve it using decomposition but could not explain the steps of composition. In addition, she had only taught 12 decomposing into 10 and 2, but not in the reverse way (i.e., decomposing 12 into 10 and 2 or 2 and 10). KHL emphasized that the subtraction was significant because it dealt with remembering. He wanted students to not only be able to calculate but also decompose it, as displayed in their discussion below:

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KHL: This topic is highly important, because it is about subtraction with borrowing. It is about the borrowing of subtracting two digits with a 1-digit number. The ones place a value of minuend as smaller than subtrahend, so [students] must remember. Therefore, most of the students must count their fingers, which is their basic calculating method. For example, [regarding] 13 - 9, where [would they] take 13 because we have only 10 fingers. However, for some students who understand, who often use their hands, they might keep 10 in mind.

SMN: Right, right, as Loui (student’s name)—he can do decomposition but cannot put the answer into the space provided. However, its result is correct; it means that he used to calculate as KHL said. He can decompose correctly, but cannot put in here, cannot explain, but his answer is correct.

KHL: Typically, if they can keep the number 10 in mind, it means that students already know decomposition. For example, [with] number 13, s/he can already see 10 and 3.

Nonetheless, now, what should we do to make students write it out, not just remember [in that way]? As for 10 and 3, as they see 10 and 3, when they subtract by 9, they will choose the larger number to subtract. Therefore, drawing a diagram is important for students. If we practice [decomposition] often, students will understand how to write decomposition…

Although the lesson on page 121 of the Grade 1 mathematics textbook was previously taught, KHL still wanted the teacher to reteach it because he was not sure if the students could really perform decomposition. Thus, the group agreed to reteach this lesson using “12 - 3” as the review of the previous lesson and adapting the exercise as the main activity. KHL, roughly, gave further suggestion that after reviewing the previous lesson, the teacher should summarize two ways of decomposition before moving to the lesson development stage, offering a hint for the students to apply when solving the main activity. During the lesson development stage, he wanted to create a word problem. He tried to collect ideas from other MTEs to design the main mathematical question. Therefore, the group decided to use a mathematical problem that students could solve using two methods of decomposition by selecting the number sentence

“15 - 7” from the exercise as the main mathematical problem in this lesson. Then, the group members had an argument about creating the word problem to suit this mathematical sentence.

They considered many possibilities: whether they would use candies or mangoes or put students’ names in the word problem to get students to feel as if it was their own problem.

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Occasionally, KHL emphasized that the teacher must ensure that the review summary of the previous lesson includes two methods of decomposition. He even advised the teacher to provide some exercises or homework to the students to practice on their own and be prepared for the next day’s lesson. The following dialogue is taken from their discussions regarding this matter.

KHL: 15 mangoes, right? For example, there are 15 mangoes; 7 mangoes are eaten. How many mangoes are left over?

VLV: For the mangoes, we can only eat, right? What else can we do?

KHL: It would be difficult [for one person] to eat 7 mangoes.

… …

KHL: Please try to think more about the word problem.

VVL: Order; find the remaining mangoes.

KHL: Will the students understand how to solve it using two methods of decomposition?

SLK; Oh no! They will not understand.

VVL: However, students can do it if they understand [during] the previous lesson’s review.

KHL: For the calculation, yes; reviewing the previous lesson is important.

… …

SMN: There are 15 mangoes; give [them] to friends.

VVL: 7 [mangoes] are eaten.

SMN: Eat 7?

VVL: Just giving [the mangoes] would be fine.

KHL: Let us suppose any names—Student A, Student B, any student’s name in this class. We can also use candy. However, please be careful with the review part, [because] it is important. When summarizing this part, the teacher must do it pleasantly. For example, 12 - 3—“Which one is subtracted by which one? Can we subtract 2 by 3? Why can we not?” We must let students say it. If they cannot do it, then, what should we do? If they cannot do it, then, we have already known 2 is less than 3. Can it be subtracted? If it cannot, because [2] is less than [3], we want to hear that [from the students]. Next, what should we do if they cannot do it? In order to know if the students understand that it is about decomposition...

SMN: Decomposition.

KHL: Now, after decomposing, we have this. For example, they can only [decompose] one way, right? The teacher must [explain to] the students that can we do this a second,

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alternative way? Put 2 here, put 10 at the front, or put 10 here and put 2 at the front.

“Can we do it or not? Why?” We want them to understand that we can put [numbers]

at any positions…when writing they can put any positions. Let us see our command question sheet. Shall we take only one [problem] or more? Will the students understand the two ways that I offer? Look at this—when summarizing the reviewing part, the teacher should say that we can write it two ways: this way, and this way.

SMN: Will the students do it in two ways on the activity sheet, as well?

KHL: Yes. Let us see. We want to see if the students can really deepen [their understanding]

when we already carefully explain that we have two ways; will they understand that these two ways below are coming from the above one? However, we are not telling them—actually, it is implicitly telling itself, but we do not tell [the students].

SMN: They would definitely be confused because they become accustomed to only putting 10 at the front.

KHL: So, you must conclude this one clearly.

SMN: Yes, of course.

KHL: Today, you provide them some homework about this, but not much—two problems for each topic. The meaning of the homework is not to write an answer; the homework is about practicing the skill.

After some long discussions, the group decided on the word problem to suit this number sentence: “Thao Itim has 15 oranges. He gives 7 oranges to his friends. How many are left over?” (see Table 23).

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Table 23. Main lesson content extracted from the lesson plan 1 of TTC2-G3.

Objectives of today’s lesson:

- Students will be able to subtract by decomposing number into 10 with any number - Students will be able to make simple diagram

Reviewing previous lesson:

Teacher lets students calculate 12 - 3 together Main activity:

Thao Itim has 15 oranges, he gives it to his friends 7 oranges, how many are left over?

Expectation

During the planning, it seemed each member already understood their role well, even if the leader had not yet assigned their duties, because they put themselves to work interactively.

For example, VLV and VVL worked together to create the one-page lesson plan; KHL and SLK helped each other create the students’ worksheets, and SMN shared ideas with the group.

The researcher observed that each member looked more skillful in his or her preparation. This is, perhaps, because—based on personal inquiry—the TTC2-G3 group already practiced a weekly lesson study of approximately 23 lessons during the 2018-2019 academic year (S.

Seomany, personal communication, August 27, 2019). Nonetheless, while other members were preparing documents, SMN—who would teach the lesson on March 19, 2019—seemed somewhat worried with her students’ performance because she often left the group to visit the classroom. Therefore, she gave some homework to the students and suggested they solve it using decomposition, because the leader of the group advised her to do so. The homework she gave to the students included the following problems: 11 - 9, 13 - 4, 15 - 3, 12 - 8, 14 - 6, 11 - 8, 13 - 9, and 12 - 3. When conducting lesson study, TTC2-G3 followed the one-page lesson plan format that was quite different from their usual lesson plan. This lesson plan was a summary of some key contents of the teaching method and main activity. It included the objective of the entire lesson, objective of the current day’s lesson, main lesson content, student thinking anticipation, teaching steps, list of materials, teaching activity (reviewing the previous lesson, four steps of open approach, warning, and homework), and planning members.

12-3 12-3

15-7 15-7

15 - 7 = 8 10 5 10-7 =3

15 - 7 = 8 5 10 10-7 =3

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